00:01
We want to know if this series is convergent.
00:04
I'm going to use the alternating series test, because it is an alternating series.
00:16
So that's the first question.
00:26
Second question is, what's the limit? so that does go to zero, as it should.
00:56
And we also have to check the ratio of successive terms.
01:19
And that limit, that goes to 1.
02:19
Which is not zero.
02:25
So therefore, it's divergent.
02:39
Yeah, so you can't be fooled just because it's alternating.
02:42
Doesn't mean it converges.
03:02
All right.
03:09
So that one diverged.
03:10
This one, we're supposed to find the interval of convergence.
03:30
All right.
03:34
So i will start with the ratio test.
03:42
When you're finding an interval of convergence, the ratio test is often the best possible possible choice.
03:50
So we got it.
04:14
So we resolve that complex fraction.
04:19
So we got n over n plus 1 times x minus 2.
04:34
So that's equal to x minus 2, the limit of n over n plus 1.
04:43
That limit is 1.
04:46
So that's x minus 2.
04:48
The ratio test tells us we have to have minus 1 less than x minus 2 less than 1.
04:58
So that means that you add 2 to both sides.
05:05
You get 1 less than x less than 3...